EQUIVALENT FRACTIONS
What Are Equivalent Fractions?
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Equivalent fractions represent the same ratio between two values.
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Fractions show a ratio between two values. The fraction ½ represents
1 out of 2. If there were 2 students sharing an assignment, each
would do part of the work. The work would be divided into 2 equal
parts and each student would do 1 part or ½ the total project.
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The fraction ½ also represents part of a set. If there are 2 cookies in a
set and one is eaten, then 1 out of 2 cookies is eaten. The relationship
between the cookie eaten and the total number of cookies is 1 out of 2
or 1/2.
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Because sets come in a variety of sizes, fractional parts will have a
variety of denominators. The fraction 1/2, for instance, has many
equivalents:
1 2 3 4 5
6
7
8
9 10 12 15 19 31 44 50 100
2 4 6 8 10 12 14 16 18 20 24 30 38 62 88 100 200
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The ratio of all the fractions in this table is 1 to 2. As a result, all the
fractions in the table are equivalents of ½.
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Any number times 1 equals itself. For example 1 x 4 = 4, 1 x 37 = 37,
1 x 576 = 576. Therefore, 1 x ½ = ½.
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Like ½, the number 1 has a multitude of equivalents: 2/2, 4/4, 10/10,
50/50. Whenever the numerator and denominator are the same
numbers, the fraction is equivalent to one.
1x5=5
3/3 x ½ = 3/6
6/6 x ½ = 6/12
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How to calculate an equivalent fraction:
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To calculate an equivalent fraction, multiply the fraction by 1 or one of
its equivalent fractions. Choose a number that when multiplied by the
denominator will produce a sum that helps you solve a problem.
For example:
1/5 = n/25
1/5 x 5/5 = 5/25
n=5
------------------------------------------------3/7 = n/21
3/7 x 3/3 = 9/21
n=9
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Calculating equivalent fractions allows us to solve a problem in which
the two fractions do not have the same denominators. For example:
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2/5 + 7/15 =
(2/5 x 3/3) + 7/15 =
6/15 + 7/15 = 13/15
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Changing the denominator of 2/5 to 15 allows us to add the two
fractions. This is accomplished by multiply 2/5 x 1 which equals 2/5,
but using 3/3 (an equivalent of 1). Any fraction can be changed to an
equivalent by multiplying times a fraction equivalent to 1.
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Permission is granted for the purchaser to print copies for non-commercial educational purposes only.
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Try This!
1. What is an equivalent fraction for 4/5?
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2. What is the numerator for this equivalent fraction?
5/8 = n/40
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3. Are 15/20 and 30/40 equivalent fractions?
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4. What is the numerator for this equivalent fraction?
21/24 = n/72
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5. Are 5/10 and 25/55 equivalent fractions?
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© Copyright NewPath Learning. All Rights Reserved.
Permission is granted for the purchaser to print copies for non-commercial educational purposes only.
Visit us at www.NewPathWorksheets.com.